Which school to apply after 10th

After completing your 10th class, you have to do the 11th class and then 12th class. You don't want mathematics. There are many groups without mathematics.
You want to go for the science stream. You can select the main subjects from Zoology, Botany, Microbiology, Biochemistry, Nutrition, Pharmacology, Psychology, Biotechnology, etc.
You can go for Arts stream also. Main subjects in this stream include History, Political Science, Economics, Geography, Sociology and Psychology.
Some good schools in your area are
1.Prof. Joseph Mundaserry Smaraka Govt, HSS, Kandassakdavi, Thrissur.
2. AKM Higher Secondary School, Poyya P.O., Thrissur, Kerala.
3. Aleemul Islam Higher Secondary School, Padoor, Thrissur
4. AM High School, Chemmanur P.O, Thrissur.
5. Chandra Memorial Government Higher Secondary School, Kuttur, Thrissur.

After completing your class tenth, you have to take up higher studies for class eleven and twelve in a well established Higher Seconday School and you are interested for the school covering state level syllabus and such schools are plenty in your locality.
Since you are interested for Psycology, this can be persued either with the combination of Arts Stream or even with the Science stream.
While taking up the subjects of Science - stream, you may take up the following combinations - Physics, Chemistry, Bilology, Microbiology, Biochemistry, Nutrition, Biotechnology, Psycology etc.
In case of selection of Arts Stream, you may have the combination of such subjects - History, Geography, Economics, Sociology, Political Science and Psycology etc.
Some of reputed schools in your locality are as follows -
1) AKM Higher Secondary School, Poyya, Thrissur- 680733, Kerala, India
Phone - 0480 - 2897600
2) AM High School, Thrissur- 680517, Kerala, India
Phone - 0485- 228940
3) Chandra Memorial Government Higher Secondary School, Thrissur- 680013, Kerala, India,
Phone - 0487- 2212569.
4) CJM Assumption Higher Secondary School, Thrissur- 680303, Kerala, India,
Phone - 0480- 2761666
5) Concord English Higher Secondary School, Panithadam, Thrissur 680604, India
Phone - 04885- 284723.

There are many schools in the Thrissur area and nearby areas where you can have options for selecting the subjects of your choice. You can get a detailed information about these schools in this site ISC itself. I am providing the list of these schools below and wherever the information is there. Contact the schools mentioned in the list below to know if they are offering science stream with Psychology and it is not mandatory to do Maths. These schools are -

1. CMS High School, Thrissur.

2. Govt SMT Higher Secondary School, Chelakkara, Thrissur.

3. St. Annes Public School, Kodakara, Thrissur.

4. Nirmala Matha Central School, Thrissur.

5. Devamatha CMI Public School, Thrissur.

6. St.Joseph's Higher Secondary School, Aloor, Thrissur.

7. St.Thomas College Higher Secondary School, Engandiyoor, Thrissur.

8. St. Pauls Public School, Kuriachira, Thrissur.

Some more schools are -
1. CMI Public School, Chalakudy, Thrissur.

2. Paramekkavu Vidya Mandir, Round East, Thrissur.

4. Kendriya Vidyalaya, Puranattukara Thrissur.

5. Chinmaya Vidyalaya, Kolazhy, Thrissur.

You can take admission in any of good schools. Some of the best schools are as hereunder.
*
The Warwin School
Instruction Medium: English
Affiliated Board: CBSE
Phone Number: 0482 626082 6, 625891
School Address: North Gate Vaikom Thrissur Distt Kerala
Email: reghunathhan@yahoo.com
India Rank : 264 out of 5595 CBSE Schools
KERALA Rank: 58 out of 499 CBSE Schools in KERALA
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Holy Cross Cbse Eng Med Res School
Instruction Medium: English
Affiliated Board: CBSE
Phone Number: 0488 521022,
FAX Number: 0141-2762864
School Address: Arthat Po Kunnamkulam Thrissur Kerala
Email: ankurshikshansanstha@gmail.com
Website: http://www.vidyasthali.com
India Rank: 259 out of 5595 CBSE Schools
KERALA Rank: 56 out of 499 CBSE Schools in KERALA
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Chinmaya Vidyalaya
Instruction Medium: English
Affiliated Board: CBSE
Phone Number: 0487 200439 2, 334454
FAX Number: 2615725
School Address: Chinmaya Gardens Kolazhy P.o. Thrissur Kerala
Email: chinvidhya@sanchernet.in
Website: http://www.cirschool.org
India Rank: 248 out of 5595 CBSE Schools
KERALA Rank: 54 out of 499 CBSE Schools in KERALA
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Don Bosco Central School
Affiliated Board: CISCE
Instruction Medium: English
School Address: Irinjalakuda Thrissur-680 121
Phone Number: 0480-2825414/072- 2821759- 2821880
Email: donboscoisc@gmail.com
India Rank: 54 out of 1914 CISCE Schools
Kerala Rank: 4 out of 133 CISCE Schools in Kerala
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Cmi Public School
Instruction Medium: English
Affiliated Board: CBSE
Phone Number: 0480 2706330 ,9447253873
FAX Number: 2700124
School Address: Chalakudy Po Thrissur Distt Kerala
Email: smundan@gmail.com
India Rank: 54 out of 5595 CBSE Schools
KERALA Rank: 11 out of 499 CBSE Schools in KERALA
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Bharatiya Vidya Bhavan's Vidya Mandir
Instruction Medium: English
Affiliated Board: CBSE
Phone Number: 0487 2370251, 2371024
FAX Number: 4872375251
School Address: Poochatty Junction Eravimangalam Po Thrissur Kerala
Email: bvmtcr@sancharnet.in
India Rank: 61 out of 5595 CBSE Schools
KERALA Rank: 12 out of 499 CBSE Schools in KERALA
*
Nirmala Matha Central School
Instruction Medium: English
Affiliated Board: CBSE
Phone Number: 0487 337904 3, 333704
School Address: East Fort Thrissur Kerala
Email: nmcst2000@sifi.com
India Rank: 105 out of 5595 CBSE Schools
KERALA Rank: 20 out of 499 CBSE Schools in KERALA
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Carmel School
Instruction Medium: English
Affiliated Board:CBSE
Phone Number: 0492 622213, 563305
School Address: Kallipadam Po Shornur Distt Palakkad Kerala
Email:principal@bhavantirupati.org
Website: www.carmelcmischoolshornur.org
India Rank:200 out of 5595 CBSE Schools
KERALA Rank: 40 out of 499 CBSE Schools in KERALA
*
Lord's Academy
Affiliated Board: CISCE
Instruction Medium: English
School Address: Cmi Icse School Varandarappilly P O Thrissur-680 303
Phone Number:0480-2760322 -2763771
Email: lordsvply@gmail.com
India Rank: 82 out of 1914 CISCE Schools
Kerala Rank: 6 out of 133 CISCE Schools in Kerala

As you will be completing your Xth std from state syllabus and is interested to take psychology in science stream without maths and residing in Thrissur district in Kerala, it may be difficult to get many +2 or Higher Secondary Science Schools/colleges for the subject and stream that you would like to opt for. I would like to list down some of the Higher Secondary Science Schools/colleges that do offer your prefered combination in Trichur and the state of Kerala and you can make your selection from the list below:
1. School Name: Govt. HSS (Nandikara- Thrissur)
School Code: 8028
Phone No.: 0480 2757086
Email ID: principal8028@gmail.com

2. School Name: Govt. HSS (Kattilapoovam - Thrissur)
School Code: 8033
Phone No.: 0487-2694239
Email ID: kattilapoovamghss@gmail.com

3. School Name: St. Mary's GHSS (Kuzhikkattussery -Thrissur)
School Code: 8064
Phone No.: 0480 2789300
Email ID: stmarys08064@rediffmail.com

4. School Name: HDPS HSS (Edathirinji - Thrissur)
School Code: 8068
Phone No.: 0480 2844740
Email ID: hdpshss@gmail.com

5. School Name: LBSM HSS (Avittathur - Thrissur)
School Code: 8069
Phone No.: 0480 2832344
Email ID: lbsm.avittathur@gmail.com

6. School Name: St. Raphel's CGHSS (Ollur - Thrissur)
School Code: 8072
Phone No.: 0487-2351510
Email ID: str2000cghssollur@gmail.com

7. School Name: CJMA HSS (Varantharapalli - Thrissur)
School Code: 8073
Phone No.: 0480 2763822
Email ID: cjmahss@gmail.com

8. School Name: Sree Sarada GHS (Puranattukara - Thrissur)
School Code: 8074
Phone No.: 0487 2306124
Email ID: sreesaradaghss@gmail.com

9. School Name: Alagappanagar Panchayath HSS (Alagappanaagar - Thrissur)
School Code: 8162
Phone No.: 0480 2750958
Email ID: aphss8162@gmail.com

10. School Name: Sree Durga Vilasam HSS ( Peramangalam - Thrissur)
School Code: 8173
Phone No.: 0487 2211755
Email ID: sdvhssperamangalam@gmail.com

11. School Name: St. Joseph s and St. Cyril s HSS (West Mangad - Thrissur)
School Code: 8176
Phone No.: 04885274190
Email ID: stjoseph.stcyrils@yahoo.com

12. School Name: St. Antony s HSS( Moorkanad - Thrissur)
School Code: 8186
Phone No.: 0480 2887864
Email ID: stantonyshssmkd10@gmail.com

13. School Name: Asha Bhavan HSS (Ollur - Thrissur)
School Code: 8193
Phone No.: 0487 2352814
Email ID: ashabhavan08@gmail.com

14. Govt. Model HSS, Ernakulam
15. St Stephen's HSS, Ernakulam
16. Govt. HSS (Areeparambu - Kottayam)
17. Baselious EM HSS (Devagiri - Kottayam)

18. Govt. HSS (Chalai - Trivandrum)
School Code: 1041
Phone No: 0471 2575722
Email ID: gmbhsschalai01041@gmail.com

19. Govt. HSS (Vellanad - Trivandrum)
School Code: 1042
Phone No: 0472 2884532
Email ID: ghssvellanad@gmail.com

Note: Most of the school/college listed above offers psychology in Arts stream, so you need to confirm from the school official site or by calling them. For more information related to +2 schools/colleges that offer your desired subject and stream can be found from the official site of Kerala i.e. http://hscap.kerala.gov.in/